Single-image super-resolution is a technique used to obtain a higher resolution image given a single low resolution image. The technique is used, for example, in the television industry when the image to be shown has to be expanded to fill the display. The technique is also used in medical applications to minimize image acquisition time where there are speed or dosage concerns. In conventional systems, single image super-resolution is performed using techniques such as interpolation and patch-based dictionary learning. State of the art results are obtained by patch based dictionary learning for sparse representation. However, for these types of methods, one needs to learn the dictionary on several training images, which makes it intractable due to high computation time and possibility of lack of training images.
Image denoising is the task of removing unwanted noise to obtain a better quality, clearer image. Denoising is especially applicable to medical imaging modalities such as ultrasound or MRI which suffer from a high acquisition noise. For CT, efficient image denoising can allow for significant dose radiation dose reduction. The image denoising problem has been addressed in several ways, such as wavelet denoising and patch-based nonlocal algorithms. Wavelet-based sparsity approaches have the benefit of carrying a regularization parameter, which adjusts the smoothness-noise balance of the resulting image. However, conventional wavelet approaches are based on a single wavelet transform. The performance of such a transform is limited due to the sparse representation limitations of a single wavelet transform. Also, regularization with a single wavelet basis may induce unwanted artifacts in the solution.